{"status": "success", "data": {"description_md": "Bernardo chooses a three-digit positive integer $N$ and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer $S$. For example, if $N = 749$, Bernardo writes the numbers $10,444$ and $3,245$, and LeRoy obtains the sum $S = 13,689$. For how many choices of $N$ are the two rightmost digits of $S$, in order, the same as those of $2N$?\n\n$\\textbf{(A)}\\ 5 \\qquad\\textbf{(B)}\\ 10 \\qquad\\textbf{(C)}\\ 15 \\qquad\\textbf{(D)}\\ 20 \\qquad\\textbf{(E)}\\ 25$", "description_html": "<p>Bernardo chooses a three-digit positive integer  <span class=\"katex--inline\">N</span>  and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers Bernardo has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer  <span class=\"katex--inline\">S</span> . For example, if  <span class=\"katex--inline\">N = 749</span> , Bernardo writes the numbers  <span class=\"katex--inline\">10,444</span>  and  <span class=\"katex--inline\">3,245</span> , and LeRoy obtains the sum  <span class=\"katex--inline\">S = 13,689</span> . For how many choices of  <span class=\"katex--inline\">N</span>  are the two rightmost digits of  <span class=\"katex--inline\">S</span> , in order, the same as those of  <span class=\"katex--inline\">2N</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 5 \\qquad\\textbf{(B)}\\ 10 \\qquad\\textbf{(C)}\\ 15 \\qquad\\textbf{(D)}\\ 20 \\qquad\\textbf{(E)}\\ 25</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2013 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/13_amc10B_p24"}}